What is "quantization"

n. 1 (context uncountable signal processing English) The process of approximating a continuous signal by a set of discrete symbols or integer values. 2 (context countable physics English) A procedure for constructing a quantum field theory starting from a classical field theory.

n. the act of dividing into quanta or expressing in terms of quantum theory [syn: quantisation]

In physics, quantization is the process of transition from a classical understanding of physical phenomena to a newer understanding known as quantum mechanics. It is a procedure for constructing a quantum field theory starting from a classical field theory. This is a generalization of the procedure for building quantum mechanics from classical mechanics. One also speaks of field quantization, as in the "quantization of the electromagnetic field", where one refers to photons as field " quanta" (for instance as light quanta). This procedure is basic to theories of particle physics, nuclear physics, condensed matter physics, and quantum optics.

__NOTOC__ Quantization is the procedure of constraining something from a continuous set of values (such as the real numbers) to a relatively small discrete set (such as the integers).

Quantization, in mathematics and digital signal processing, is the process of mapping a large set of input values to a (countable) smaller set. Rounding and truncation are typical examples of quantization processes. Quantization is involved to some degree in nearly all digital signal processing, as the process of representing a signal in digital form ordinarily involves rounding. Quantization also forms the core of essentially all lossy compression algorithms. The difference between an input value and its quantized value (such as round-off error) is referred to as quantization error. A device or algorithmic function that performs quantization is called a quantizer. An analog-to-digital converter is an example of a quantizer.

Quantization, involved in image processing, is a lossy compression technique achieved by compressing a range of values to a single quantum value. When the number of discrete symbols in a given stream is reduced, the stream becomes more compressible. For example, reducing the number of colors required to represent a digital image makes it possible to reduce its file size. Specific applications include DCT data quantization in JPEG and DWT data quantization in JPEG 2000.

In linguistics, a quantized expression is such that, whenever it is true of some entity, it is not true of any proper subparts of that entity. Example: If something is an "apple", then no proper subpart of that thing is an "apple". If something is "water", then many of its subparts will also be "water". Hence, "apple" is quantized, while "water" is not. Quantization has proven relevant to the proper characterization of grammatical telicity (roughly, sentences that present events as bounded/unbounded in time) and the mass/count distinction for nouns. The notion was first applied to linguistic semantics by the linguist Manfred Krifka.

Formally, a quantization predicate QUA can be defined as follows, where U is the universe of discourse, and F is a variable over sets, and p is a mereological part structure on U with  <  the mereological part-of relation.

(∀F ⊆ U)(QUA(F) ⇔ (∀x, y)(F(x) ∧ F(y) ⇒ ¬x < y))

In digital music processing technology, quantization is the process of transforming performed musical notes, which may have some imprecision due to expressive performance, to an underlying musical representation that eliminates this imprecision. The process results in notes being set on beats and on exact fractions of beats. The most difficult problem in quantization is determining which rhythmic fluctuations are imprecise or expressive (and should be removed by the quantization process) and which should be represented in the output score. For instance, a simple children's song should probably have very coarse quantization, resulting in few different outputted notes. On the other hand, quantizing a performance of a piano piece by Arnold Schoenberg, for instance, should result in many smaller notes, tuplets, etc.

A frequent application of quantization in this context lies within MIDI application software or hardware. MIDI sequencers typically include quantization in their manifest of edit commands. In this case, the dimensions of this timing grid are set beforehand. When one instructs the music application to quantize a certain group of MIDI notes in a song, the program moves each note to the closest point on the timing grid.

The purpose of quantization in music processing is to provide a more beat-accurate timing of sounds. Quantization is frequently applied to a record of MIDI notes created by the use of a musical keyboard or drum machine.

Quantization in MIDI is usually applied to Note On messages and sometimes Note Off messages; some digital audio workstations shift the entire note by moving both messages together. Sometimes quantization is applied in terms of a percentage, to partially align the notes to a certain beat. Using a percentage of quantization allows for the subtle preservation of some natural human timing nuances.

In recent years audio quantization has come into play, with the plug in Beat Detective on all versions of Pro Tools being used regularly on modern day records to tighten the playing of drums, guitar, bass, etc.

The phrase "pitch quantization" can refer to pitch correction used in audio production, such as using Auto-Tune.